Econometrics project Is there a gender gap in mathematicsrecherche.enac.fr/~steve.lawford/teaching_papers/example_projects/... · Bastien CHIRAT - Valentin LELEU-LAMBOUR Econometrics

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IntroductionFirst study

Second ModelThird ModelConclusion

Econometrics projectIs there a gender gap in mathematics ?

Bastien CHIRAT - Valentin LELEU-LAMBOUR

ENAC

12/04/16

Bastien CHIRAT - Valentin LELEU-LAMBOUR Econometrics project Is there a gender gap in mathematics ?

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Introduction

We use data on the individual results in the InternationalMathematical Olympiad for the year 2015 (cross-sectional data).The purpose of the study is to bring some evidence (if they exist !)there is a gender gap in this field, and that guys are more able inmathematics than girls.


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Some clarifications :

If we analyse the I.M.O. individual results, we cannot pretendthat our study concerns every students. I.M.O. is for elitestudents, so if we show that it exists a gender gap and if wequantify its influence on results, our demonstration will bevalid only for elite. If we wanted generalize, we should usemore data.

We interest only on individual results, we won’t take intoaccount or analyse team results or collective parameters’influences.

We have studied the results for the year 2015, we have chosennot to analyse the influence of time on results. Why ?Because we have privileged the parameters for the study


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The rules

The Olympiad gathers teams of many countries around theworld (104 countries in 2015). The teams are composed of 6high school students max.

Each student faces 6 different problems during 2 days.

Each problem can bring a maximum of 7 points.

So, we can win a maximum of 42 points in total. The rank isdone comparing the total number of points of each student.

Now, the context is done : Let’s start !


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Choice of variables

Number of variables: k=12

Explanatory variables DetailsGender =1 if manAsian =1 if asian sounding nameTotal total pointsRank rank of the studentsNbpart number of previous participationsCountry rank of the countryPlace =1 if Country=12IDH HDI [0, 1]Maths country ranking by maths levelInnovation country ranking by innovationPIB/hab (*100) dollars/yrPop (∗106) by country


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The parameter Gender

As a first analyse, it appearsthat there are much more guyswho participate than girls.Can we consider that itconstitutes a first evidencethat guys are more talented inmathematics than girls ?

Figure: Gender variable


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The first regression

For our first study, we wanted to see the influence of gender ontotal without considering any other parameter.

Equation 1

Total = β0 +β1Gender +u


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EViews Results

Figure: EViews Result for Equation 01Bastien CHIRAT - Valentin LELEU-LAMBOUR Econometrics project Is there a gender gap in mathematics ?

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Validity of the model

Evolution of our model :Our first model is very simple and just gives us an idea about theeffect of gender (positive effect) and considering its value, being aguy brings nearly 5 points on total. Nevertheless, the R-squared isvery low (0.025), so we have to go further to understand themechanisms hiding behind this variable.


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Second Equation

We decided to add all the variables to see their effect onTotal.

Equation 2

Total = β0 +β1Asian +β2Gender +β3Nbpart +β4Place +β5IDH+β6Math +β7Innov +β9PIB +β10Pop +u


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EViews Results

Figure: EViews result for Equation 2Bastien CHIRAT - Valentin LELEU-LAMBOUR Econometrics project Is there a gender gap in mathematics ?

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Interpretation

Variables Significant Concrete consequencesAsian 99 +4.63pts if your name sounds asianGender 99 +3.71pts if you are a manNbpart 99 +2.54pts by previous participationPlace 95 +6ptsif student is ThaiIDH NO +5.5pts if HDI increases by 0.5Math 90 +0.023pts by math ranking pointInnov 95 -0.18pts by innovation ranking pointPIB/hab NO -0.0012ptsif GDP inscreases by 100dollars/yrPop 99 +0.013pts if pop inscreases by a million

Finally, we notice that Adjusted R-squared is equal to 0.29. Wehave a more precise model, but it is far from perfect !


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Third Equation

If we observe the header, we see that there are 346 includedobservations on 577 individuals, because it misses data of somecountries for the innovation index and the rank in mathematics.By ignoring these two variables we throw away high correlatedparameters.In order to optimize N and considering the results of theregression, we have chosen to perform a regression without innovand math parameters..

Equation 3

Total = β0 +β1Asian +β2Gender +β3Nbpart +β4Place +β5IDH+β6PIB +β7Pop +u


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EViews Results

Figure: EViews result for Equation 3


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Interpretation

Variables Significant Concrete consequencesAsian 99 +6.51pts if your name sounds asianGender 99 +2.78pts if you are a manNbpart 99 +2.58ptsby previous participationPlace 95 +6.88pts if student is ThaiIDH 99 +16.68pts if HDI increases by 0.5PIB/hab 99 -0.009pts if GDP inscreases by 100dollars/yrPop 99 +0.011pts if pop inscreases by a million

This is getting better ! Adjusted R-squared is higher (0.337). Thevalues have changed a little.


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Normality of the errors

Let’s perform a test of normality of residuals to know if we can useOrdinary Least Squares and if we conserve the classicalassumptions.

Figure: Histogramm of the errors


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Normality of the errors

From the Jarque-Bera test we reject normality of the errors at 99percent level.So, for the upcoming analyses, we won’t work with the classicalassumptions and we will have to be careful with the tests we use.


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Some evidence of heteroscedasticity

Does our model presentheteroscedasticity ? Let’sanalyse the graph :It seems that there is some !The lines show that varianceof errors are not constant,which constitutes an evidenceof heteroscedasticity.


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Some evidence of heteroscedasticity

The White test confirms thishypothesis : we rejecthomoscedasticity at 99 percentlevel (Chi- Square probability).So now, we should work withWhite Standard Errors.


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Final regression

The purpose of this regressionis to see the influence ofgender on all otherparameters. The AdjustedR-squared is nearly the sameas for the previous regressionbut what about theprobabilities associated ?!


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Final regression

With this new regression, wehave won in precision(Adjusted R-squared = 0.38,the best one!).But we notice that genderparameter continues to lossinfluence (2.43) while theprecision of the model isincreasing. With this model,being a guy allows to win only2.43 points more.


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Conclusion

If we try to answer to the question, our study shows thatgender parameter has an influence on the final result.Nevertheless, it has a limited importance and doesn’tconstitute the main characteristics of the winners.The main problem is that even if we try to quantify precisely theelements which conduct a candidate to win, it’s impossible to takeinto account mood, fatigue, stress which are probably very influenton the final result.With more time, an interesting study would have been to performregressions considering the years. Maybe we would have noticed anevolution of some parameters’ influences, as the gender one...


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Econometrics project Is there a gender gap in mathematicsrecherche.enac.fr/~steve.lawford/teaching_papers/example_projects/... · Bastien CHIRAT - Valentin LELEU-LAMBOUR Econometrics